Method for calibrating a volumetric flow meter having an array of sensors

ABSTRACT

A method and apparatus are provided for calibrating a flow meter having an array of sensors arranged in relation to a pipe that measures a flow rate of a fluid flowing in the pipe. The method features the step of calibrating the flow rate using a calibration correction function based on one or more parameters that characterize either the array of sensors, the pipe, the fluid flowing in the pipe, or some combination thereof. The calibration correction function depends on either a ratio t/D of the pipe wall thickness (t) and the pipe inner diameter (D); a ratio t/λ of the pipe wall thickness (t) and the eddie wavelength (λ) of the fluid; a Reynolds number (ρUD/μ) that characterizes the fluid flow in the pipe; a ratio Δx/D of the sensor spacing (Δx) and the pipe inner diameter (D); a ratio fΔx/U meas  of usable frequencies in relation to the sensor spacing (Δx) and the raw flow rate (U meas ); or some combination thereof. The apparatus takes the form of a flow meter having a calibration correction function module performing the aforementioned functionality.

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

This application is a continuation patent application of U.S. patentapplication Ser. No. 10/720,599, filed Nov. 24, 2003; now U.S. Pat. No.7,139,667 which claimed the benefit to U.S. provisional patentapplication Ser. No. 60/428,312, filed Nov. 22, 2002; U.S. provisionalpatent application Ser. No. 60/510,765, filed Oct. 9, 2003; and U.S.provisional patent application Ser. No. 60/511,399, filed Oct. 15, 2003,which are all hereby incorporated by reference in their entirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to flow meters; and more particularly to amethod and apparatus for calibrating a flow meter having an array ofsensors arranged in relation to a pipe that measures a flow rate of afluid flowing in the pipe.

2. Description of the Related Art

Volumetric flow measurement plays a critical role in processoptimization and control of most industrial processes. The currentindustrial flow measurement market is often segmented into two broadtechnology categories: old technology and new technology flow meters.Old technology flow meters include flow measurement technologies thathave been in used for greater than 70 years and include turbine meters,orifice plates and variable area flow meters. The new technology flowmeters have emerged over the last 30˜50 years and offer advantages overthe old technologies in performance, functionality, and reliability. Themajor types of new technology flow meters include ultrasonic meters,electromagnetic flow meters, vortex flow meters, and coriolis flowmeters. Each type has evolved to serve various aspects of the diverserange of applications within the industrial flow meter landscape. Forexample, the electromagnetic flow meter has emerged as the dominate typeof flow meter used in the paper and pulp industry.

In particular, flow meters having an array of sensors arranged inrelation to a pipe that measure a flow rate of a fluid flowing in thepipe are known in the art. For example, U.S. Pat. No. 6,609,069, whichis incorporated by reference, discloses a method and apparatus fordetermining the flow velocity of fluid within a pipe, such as an oilpipe.

One problem with flow meters in the art is that, despite the fact thatthey are calibrated to measure a flow rate of a given fluid(s) flowingin a given pipe(s), this calibration may not be correct when the flowmeter is used in the field to measure different types of fluids flowing,for example, in different types of pipes than those in which the flowmeter was originally calibrated to measure fluid flow. For example, theoriginal calibration is likely to provide an incorrect measurement whenthe flow meter is used in relation to a fluid having a different densityor viscosity than it was originally calibrated, or when the flow meteris used in relation to a pipe having a different wall thickness or innerdiameter than it was originally calibrated, or when the array of sensorsare spaced differently in relation to the pipe than it was originallycalibrated. In view of this, the known flow meters are likely to have anerror in their measurement, for which no correction is made. Moreover,the known flow meters are not designed to correct the originalcalibration based on one or more parameters that characterize either thearray of sensors, the pipe, the fluid flowing in the pipe, or somecombination thereof.

There is a need in the prior art for a flow meter that can be calibratedin the field based on receiving such parameters.

SUMMARY OF THE INVENTION

The present invention provides a new and unique method and apparatus forcalibrating a flow meter having an array of sensors arranged in relationto a pipe that measures a flow rate of a fluid flowing in the pipe. Themethod features the step of calibrating the flow rate using acalibration correction function based on one or more parameters thatcharacterize either the array of sensors, the pipe, the fluid flowing inthe pipe, or some combination thereof. The calibration correctionfunction depends on either a ratio t/D of the pipe wall thickness (t)and the pipe inner diameter (D); a Reynolds number (ρUD/μ) thatcharacterizes the fluid flow in the pipe; a ratio Δx/D of the sensorspacing (Δx) and the pipe inner diameter (D); a ratio fΔx/U_(means) ofusable frequencies in relation to the sensor spacing (Δx) and the rawflow rate (U_(meas)); or some combination thereof. The apparatus takesthe form of a flow meter having a calibration correction function moduleperforming the aforementioned functionality.

The Reynolds number (Re), based on pipe diameter (D), characterizes manyof the engineering properties of the flow. The Reynolds number is anon-dimensional ratio representing the relative importance of inertialforces to viscous forces within a flow:

${Re} = {{\frac{inertial}{viscous}{forces}} = {\frac{\rho\; u\frac{\partial u}{\partial x}}{\mu\frac{\partial^{2}u}{\partial y^{2}}} = \frac{UD}{v}}}$Where ρ is the fluid density, μ is the dynamic viscosity, U is thevolumetrically averaged flow velocity and v (=μ/ρ) is the kinematicviscosity. The critical Reynolds number for pipe flows, above whichflows are considered turbulent, is ˜2,300. Most flows in the paper andpulp industry have Reynolds number ranging from one hundred thousand toseveral million, well within the turbulent regime. In addition todemarcating a boundary between laminar and turbulent flow regimes, theReynolds number is a similarity parameter for pipe flows, i.e. flows ingeometrically similar pipes with the same Reynolds number aredynamically similar.

The flow rate being calibrated may include a volumetric flow rate (Q) ora velocity of flow. In operation, the volumetric flow rate (Q) isdetermined based on the equation:Q=A*U _(av),where A is a cross sectional area of the pipe's inner diameter andU_(av) is an average flow velocity.

The average flow velocity (U_(av)) is determined based on the equation:U _(av)=the calibration correction function*U _(meas),where U_(means) is a measured flow rate.

The velocity of flow is determined by using a K-ω plot.

The array of sensors includes an array of pressure sensors, as well asan array of strain or temperature sensors.

One advantage of the present invention is that the flow meter accordingto the present invention can be calibrated in the field based onreceiving the one or more parameters that characterize either the arrayof sensors, the pipe, the fluid flowing in the pipe, or some combinationthereof.

Another advantage of the present invention is that the flow meteraccording to the present invention provides a more accurate measurementafter being calibrated in the field.

Still another advantage of the present invention is that the flow meteraccording to the present invention can be designed and used in relationto a class of pipes, such as Sch 10 or 40, and calibrated in the fieldbased on a family of calibration curves.

In one particular application of the present invention relates toproviding a new flow measurement technology well-suited for the paperand pulp industry. The present invention provides robust, high-accuracy,volumetric flow rate measurement for a broad range of single andmultiphase flows. The present invention can be implemented with portedpressure transducers or with non-intrusive sensors clamped-on toexisting process piping. This first-principles flow measurementmethodology utilizes an array of sensors to listen to the unsteadypressure field within standard process flow lines. Sonar arrayprocessing techniques are employed to track the speed at which coherentstructures, inherent within the turbulent pipe flow of the processfluid, convect past the sensor array. The present invention results in ameter performance on paper and pulp slurries ranging from 0-5% pulp.Results from a single phase calibration facility are also presenteddemonstrating 0.5% accuracy for pipes ranging from 3 to 16 inches indiameter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a flow meter having an array of sensorsdisposed axially along a pipe for measuring the volumetric flow of theprocess flow flowing in the pipe, in accordance with the presentinvention.

FIG. 2 is a cross-sectional view of a pipe with fluid flowing thereinhaving an array of pressure sensors disposed axially along the pipe, inaccordance with the present invention.

FIG. 3 is a flow chart illustrative of the algorithm of the signalprocessor, in accordance with the present invention.

FIG. 4 is a k-w plot showing a convective ridge illustrative of theconvective flow within the pipe, in accordance with the presentinvention.

FIG. 5 is a graph of an attenuation profile showing a dependence of aratio of the pipe wall thickness (t) in relation to the pipe innerdiameter (D).

FIG. 6 is a graph showing a dependence of the Reynolds number (Re) inrelation to an offset (%) of the flow velocity.

FIG. 7 is a graph of the Reynolds number (Re) in relation to an offset(%) of the flow velocity showing a dependence of the sensor spacing andinner pipe diameter.

FIG. 8, including FIGS. 8 a, 8 b, 8 c, show . . . .

FIG. 9 is a graph of the Reynolds number (Re) in relation to an offset(%) of the flow velocity in the form of a family of calibration curves.

BEST MODE FOR CARRYING OUT THE INVENTION

FIGS. 1 and 2 show a flow meter generally shown as 10 that measures theflow rate, including the volumetric flow rate and flow velocity, of asingle phase fluid 12 (e.g., gas and liquid) and/or a multi-phasemixture 12 (e.g., process flow) flowing through a pipe 14 shown in FIG.2. The multi-phase mixture may be a two-phase liquid/vapor mixture, asolid/vapor mixture or a solid/liquid mixture, gas entrained liquid or athree-phase mixture. The scope of the invention is not intended to belimited to the type or kind of fluid, flow, media or mixture beingmeasured by the flow meter 10, or the type or kind of the pipe 14 inwhich the fluid, flow, media or mixture is flowing.

The flow meter 10 includes a sensing device 16 comprising an array ofpressure sensors (or transducers) 18-21 spaced axially along the outersurface 22 of the pipe 14 (FIG. 2), having a process flow 12 propagatingtherein. The pressure sensors 18-21 measure the unsteady pressuresproduced by vortical disturbances 118 (FIG. 2) within the pipe 14, whichare indicative of the velocity of the process flow 12. The outputsignals (P₁(t)-P_(N)(t)) may be conditioned in one or more ways,including amplified and/or converted in an analog-to-digital (A/D)converter, although the scope of the invention is not intended to belimited to any such conditioning.

The output signals (P₁(t)-P_(N)(t)) of the pressure sensors 18-21 arethen provided to a processor 24, which processes the pressuremeasurement data to determine the volumetric flow rate and flowvelocity. The measurements are derive by the processor 24 byinterpreting the unsteady pressure field within the process piping usingmultiple transducers/sensors displaced axially over about 2 diameters inlength. The processor 24, including the modules and functionalitydescribed herein, may be implemented using hardware, software or acombination thereof. One software embodiment envisioned comprises, amongother things, a microprocessor based architecture having amicroprocessor, memory, input/output devices and address and data buscoupling the same. A person skilled in the art would be able toimplement the processor 24 without undue experimentation. The flowmeasurements can be performed using ported pressure transducers orclamp-on, strain-based sensors.

The flow meter 10 measures the volumetric flow rate by determining thevelocity of vortical disturbances or “eddies” 118 (FIG. 2) propagatingthrough the flow 12 using the array of pressure sensors 18-21. Similarto that shown in U.S. patent application Ser. No. 10/007,736 filed Nov.8, 2001. The flow meter 10 measures the velocities associated withunsteady flow fields and/or pressure disturbances created by thevortical disturbances or “eddies” 118 to determine the velocity of theflow 12. The pressure sensors 18-21 measure the unsteady pressuresP₁(t)-P_(N)(t) created by the vortical disturbances 118 as thesedisturbances convect within the flow 12 through the pipe 14 in a knownmanner. Therefore, the velocity of these vortical disturbances 118 isrelated to the velocity of the flow 12 and hence the volumetric flowrate may be determined, as will be described in greater detailhereinafter.

The Pressure Sensors 18-21

In FIG. 1, each of the pressure sensors 18-21 may include apiezoelectric film sensor to measure the unsteady pressures of the flow12. The piezoelectric film sensors include a piezoelectric material orfilm to generate an electrical signal proportional to the degree thatthe material is mechanically deformed or stressed. The piezoelectricsensing element is typically conformed to allow complete or nearlycomplete circumferential measurement of induced strain to provide acircumferential-averaged pressure signal. The sensors can be formed fromPVDF films, co-polymer films, or flexible PZT sensors, similar to thatdescribed in “Piezo Film Sensors Technical Manual” provided byMeasurement Specialties, Inc., which is incorporated herein byreference. A piezoelectric film sensor that may be used for the presentinvention is part number 1-1002405-0, LDT4-028K, manufactured byMeasurement Specialties, Inc.

Piezoelectric film (“piezofilm”), like piezoelectric material, is adynamic material that develops an electrical charge proportional to achange in mechanical stress. Consequently, the piezoelectric materialmeasures the strain induced within the pipe 14 due to unsteady pressurevariations (e.g., vortical disturbances) within the process flow 12.Strain within the pipe is transduced to an output voltage or current bythe attached piezoelectric sensor. The piezoelectrical material or filmmay be formed of a polymer, such as polarized fluoropolymer,polyvinylidene fluoride (PVDF). The piezoelectric film sensors aresimilar to that described in U.S. patent application Ser. No. 10/712,833which is incorporated herein by reference.

The scope of the invention is not intended to be limited to the kind ortype of pressure sensors 18-21.

The Measurement of Volumetric Flow

To measure volumetric flow, the flow meter 10 characterizes the velocityat which the coherent vortical structures 118 convect past the axialarray of sensors 18-21. Coherent structures 118 are an inherent featureof turbulent boundary layers present in all turbulent flows. Unlikeconventional vortex shedding meters, no internal geometry is required togenerate these structures.

The overwhelming majority of industrial process flows involve turbulentflow 12. Turbulent fluctuations within the process flow govern many ofthe flow properties of practical interest including the pressure drop,heat transfer, and mixing. For engineering applications, consideringonly the time-averaged properties of turbulent flows is often sufficientfor design purposes. For sonar based array processing flow meteringtechnology, understanding the time-averaged velocity profile inturbulent flow 12 provides a means to interpret the relationship betweenspeed at which the coherent structures 118 convect and thevolumetrically averaged flow rate.

Turbulent pipe flows 12 are highly complex flows. Predicting the detailsof any turbulent flow is problematic, however, much is known regardingthe statistical properties of the flow. The maximum length scale of theeddies 118 is set by the diameter of the pipe 14. These structures 118remain coherent for several pipe diameters downstream, eventuallybreaking down into progressively smaller eddies until the energy isdissipated by viscous effects.

Experimental investigations have established that eddies generatedwithin turbulent boundary layers convect at roughly 80% of maximum flowvelocity. For pipe flows, this implies that turbulent eddies willconvect at approximately the volumetrically averaged flow velocitywithin the pipe 14. The precise relationship between the convectionspeed of the turbulent eddies 118 and the flow rate for each class ofmeters can be calibrated empirically as described below.

In FIG. 2, the relevant flow features of the turbulent pipe flow 12 areillustrated along with the axial array of sensors 18-21. As shown, thetime-averaged axial velocity is a function of radial position, from zeroat the wall to a maximum at the centerline of the pipe. The flow 12 nearthe wall is characterized by steep velocity gradients and transitions torelatively uniform core flow near the center of the pipe 14. Vorticalstructures 118 are superimposed over time averaged velocity profile.These coherent structures contain temporally and spatially randomfluctuations with magnitudes typically less than 10% percent of the meanflow velocity and are carried along with the mean flow. Experimentalinvestigations have established that the eddies 118 generated withinturbulent boundary layers remain coherent for several pipe diameters andconvect at roughly 80% of maximum flow velocity.

From a volumetric flow measurement perspective, the volumetricallyaveraged flow velocity is of interest. The volumetrically averaged flowvelocity, defined as the total volumetric flow rate, Q, divided by thecross sectional area of the conduit, A, is a useful, but arbitrarilydefined property of the flow. In fact, given the velocity profile withinthe pipe, little flow is actually moving at this speed. The preciserelationship between the convection speed of turbulent eddies and theflow rate is determined experimentally through calibration for each.

The Calibration Correction Module 38

The processor 24 includes a calibration correction function module 38for calibrating the flow rate using a calibration correction functionbased on one or more parameters that characterize either the array ofsensors 18-21, the pipe 14, the fluid 12 flowing in the pipe 14, or somecombination thereof. The calibration correction function depends oneither a ratio t/D of the pipe wall thickness (t) and the pipe innerdiameter (D); a Reynolds number (ρUD/μ) that characterizes the fluidflow in the pipe; a ratio Δx/D of the sensor spacing (Δx) and the pipeinner diameter (D); a ratio fΔx/U_(means) of usable frequencies inrelation to the sensor spacing (Δx) and the raw flow rate (U_(meas)); orsome combination thereof.

The Reynolds number, based on pipe diameter, characterizes many of theengineering properties of the flow. The Reynolds number is anon-dimensional ratio representing the relative importance of inertialforces to viscous forces within a flow:

${Re} = {{\frac{inertial}{viscous}{forces}} = {\frac{\rho\; u\frac{\partial u}{\partial x}}{\mu\frac{\partial^{2}u}{\partial y^{2}}} = \frac{UD}{v}}}$

Where ρ is the fluid density, μ is the dynamic viscosity, U is thevolumetrically averaged flow velocity and v (=μ/ρ) is the kinematicviscosity. Pipe flows with Reynolds numbers exceeding a critical value,typically ˜2300, are turbulent. Those with Reynolds numbers below thisvalue are laminar.

The calibration correction function module 38 may be implemented usinghardware, software or a combination thereof. One software embodimentenvisioned comprises, among other things, a microprocessor basedarchitecture having a microprocessor, memory, input/output devices andaddress and data bus coupling the same. A person skilled in the artwould be able to implement the calibration correction function module 38without undue experimentation.

The flow rate includes a volumetric flow rate (Q) and the calibrationcorrection function module 38 determines the volumetric flow rate (Q)indicated as 40′ based on the equation:Q=A*U _(av),where A is a cross sectional area of the pipe's inner diameter andU_(av) is an average flow velocity. The average flow velocity (U_(av))is determined based on the equation:U _(av)=the calibration correction function*U _(meas),where U_(meas) is a measured flow rate.

The Reynolds number ρUD/μ is defined by a ratio of the fluid density(ρ), the volumetrically averaged flow velocity (U) and the pipe innerdiameter (D) in relation to the dynamic viscosity of the fluid (μ).

The calibration correction function module 38 also may receive as inputsone or more parameters via line 38 a, consistent with that discussedbelow.

FIG. 3: The Basic Steps

FIG. 3 shows the basic steps generally indicated as 46 performed by theprocessor 24 in FIG. 1, including a step 48 for performing an FFT ofpressure signals P₁(t)-P_(N)(t); a step 50 for determining power of thepressure signals in a K-ω plane; a step 52 for determining a convectiveridge in the K-ω plane; a step 54 for calculating velocity of flow(Vc(t)) and/or volumetric flow (VF); and a step 62 for calibrating thevelocity of flow (Vc(t) and/or volumetric flow (VF). The step 48 isperformed by the FFT modules 30-33; the steps 50, 52, 54 are performedby the array processor 36 and the step 62 is performed by thecalibration correction function module 38.

In FIG. 1, the flow meter 10 has an array of at least three acousticpressure sensors 18-21, located at three locations x₁, X₂, X₃ axiallyalong the pipe 14. One will appreciate that the sensor array may includemore than three pressure sensors as depicted by pressure sensor 21 atlocation X_(N). For example, the array of sensors may include at least4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, or 16 sensors. The pressuregenerated by the vortical disturbances 118 may be measured throughpressure sensors 18-21. The pressure sensors provide pressuretime-varying signals P₁(t), P₂(t), P₃(t), P_(N)(t) to a signal processor24 to known Fast Fourier Transform (FFT) logics 30-33, respectively. TheFFT logics 30-33 calculate the Fourier transform of the tune-based inputsignals P₁(t)-P_(N)(t) and provide complex frequency domain (orfrequency based) signals P₁(ω) P₂(ω), P₃(ω), P_(N)(ω) indicative of thefrequency content of the input signals. Instead of FFT's, any othertechnique for obtaining the frequency domain characteristics of thesignals P₁(t)-P_(N)(t) may be used.

The frequency signals P₁(ω)-P_(N)(ω) are fed to an array processor 36,which provides a flow signal 40 indicative of the volumetric flow rateof the process flow 12 and a velocity signal 42 indicative of thevelocity of the process flow.

One technique of determining the convection velocity of the vorticaldisturbances 118 within the process flow 12 is by characterizing theconvective ridge of the vortical disturbances using an array of unsteadypressure sensors or other beam forming techniques, similar to that shownin U.S. Pat. No. 6,609,069, entitled “Method and Apparatus forDetermining the Flow Velocity Within a Pipe”, which is incorporatedherein by reference.

The flow metering methodology uses the convection velocity of coherentstructure with turbulent pipe flows 12 to determine the volumetric flowrate. The convection velocity of these eddies 118 is determined byapplying arraying processing techniques to determine the speed at whichthe eddies convect past an axial array of unsteady pressure measurementsdistributed along the pipe 14, similar to that used in the radar andsonar fields.

The array processing algorithms determine the speed of the eddies 118 bycharacterizing both the temporal and spatially frequency characteristicsof the flow field. For a series of coherent eddies convecting past afixed array of sensors, the temporal and spatial frequency content ofpressure fluctuations are related through the following relationship:

$k = \frac{\omega}{U_{convect}}$Here k is the wave number, defined as k=2π/λ and has units of 1/length,ω is the temporal frequency in rad/sec, and U_(convect) is theconvection velocity. Thus, the shorter the wavelength (larger k) is, thehigher the temporal frequency.

In array processing, the spatial/temporal frequency content of timestationary sound fields are often displayed using “k-ω plots”. K-ω plotsare essentially three-dimensional power spectra in which the power of asound field is decomposed into bins corresponding to specific spatialwave numbers and temporal frequencies. On a K-ω plot, the powerassociated with a pressure field convecting with the flow is distributedin regions, which satisfies the dispersion relationship developed above.This region is termed “the convective ridge” and the slope of this ridgeon a K-ω plot indicates the convective velocity of the pressure field.This suggests that the convective velocity of turbulent eddies, andhence flow rate within a pipe, can be determined from the output of aphased array of sensor and identifying the slope of the convective ridgewithin the K-ω plane.

FIG. 4: The K-ω plot

FIG. 4 shows an example of a K-ω plot generated from a phased array ofpressure sensors 18-21. The power contours show a well-definedconvective ridge. A parametric optimization method was used to determinethe “best” line representing the slope of the convective ridge 200. Forthis case, a slope of 14.2 ft/sec was determined. The intermediateresult of the optimization procedure is displayed in the insert, showingthat optimized value is a unique and well-defined optima.

The K-ω plot shown in FIG. 4 illustrates the fundamental principlebehind sonar based flow measure, namely that axial arrays of sensors canbe used in conjunction with sonar array processing techniques todetermine the speed at which naturally occurring turbulent eddiesconvect within a pipe.

The Volumetric Flow Rate

The volumetric flow rate for a given pipe is defined as follows:Q=A·U _(av)Where:

-   -   A=Cross sectional area of the pipe's inner diameter    -   U_(av)=Average velocity of the flow profile within the pipe

As described herein before, the average velocity is defined as follows:

$U_{av} = {f{\{ {\frac{t}{D};\frac{\rho\;{UD}}{\mu};\frac{\Delta\; x}{D};\frac{f\;\Delta\; x}{U_{meas}}} \} \cdot U_{meas}}}$Where: U_(meas) = raw flow rate as determined by the algorithmf  {  } = calibration correction function$\frac{t}{D} = {\text{ratio of pipe wall thickness(}\text{t}\text{) and pipe inner diameter(}\text{D}\text{)}}$$\frac{\rho\;{UD}}{\mu} = \text{Reynolds Number}$$\frac{\Delta\; x}{D} = {{dependence}\mspace{14mu}{on}\mspace{14mu}{the}\mspace{14mu}{ratio}\mspace{14mu}{of}\mspace{14mu}{sensor}\mspace{14mu}{{spacing}( {\Delta\; x} )}\mspace{14mu}{and}}$the  inner  diameter  of  the  pipe(D)$\frac{f\;\Delta\; x}{U_{meas}} = {{dependence}\mspace{14mu}{on}\mspace{14mu}{the}\mspace{14mu}{useable}\mspace{14mu}{{frequencies}(f)}}$within  the  array  response

FIGS. 5-7 provide graphs of empirical testing that has been conducted todetermine the correction function dependence on each of the contributingparameters.

FIG. 5: The Pipe Wall Thickness (t) to Pipe Inner Diameter (D)Dependence

FIG. 5 shows a graph indicating an attenuation profile in relation tothe dependence of the pipe wall thickness (t) to pipe inner diameter(D). In effect, the unsteady pressure fluctuations created by theconvecting field of eddies strain the pipe at a corresponding set offrequencies. These are proportional to the wavelength of the eddies. Thepipe wall acts as an attenuator and will decrease the signal power as afunction of the wall thickness and frequency.

The Attenuation Characteristics

The attenuation characteristics of the pipe wall change as a function ofthe ratio of the wall thickness to the inner diameter.

FIG. 6: The Reynolds Number Dependence

FIG. 6 shows the measured velocity of the flow is a function of theReynolds Number. The graph provides a set of empirical datademonstrating this effect: The Reynolds Number effects the velocityprofile and therefore the distribution of the velocity across thediameter of the pipe.

FIG. 7: The Sensor Spacing to Pipe Inner Diameter (D) Dependence

FIG. 7 is a graph of empirical data showing the dependence between thesensor spacing (Δx) and pipe inner diameter (D). In effect, the sensorspacing (Δx) defines the wavelength, or alternatively the wave number,of the signals to be measured through the dispersion relationship. Thisestablishes the size of the vortical signals that can be measured. Theconvective velocity of this set of vorticals has a unique relationshipto the average volumetric flow rate.

The Dependence of Usable Frequencies within the Array Response

The sensor spacing Δx defines the wavelength, or alternatively the wavenumber, of the signals to be measured through the dispersionrelationship. The

$\frac{f\;\Delta\; x}{U_{meas}}$ratio defines which of the measurable wavelengths should be used at agiven flow rate. For the previously described empirical testing, theminimum and maximum values were set to 0.3 and 0.7 respectively.

FIG. 8 a shows a dimensional K-ω plot; FIG. 8 b shows an array gain; andFIG. 8 c shows a non-dimensional K-ω plot.

Using the parameter fΔx/U where f is the frequency in Hz (f=_(ω)/(2π)where _(ω) is the frequency in rad/sec) enables the k-_(ω) plot to benon-dimensionalized. This results in the ability to use the same regionof the array gain function regardless of the velocity. This same regionis preferably centered about the point of maximum array response (π/Δk)of the array gain function. (For example, per the attached figure themaximum array response occurs at k=π/Δx. Keeping in mind the dispersionrelationship k=_(ω)/u=2πf/u the maximum array response will occur atdifferent frequencies for different velocities. That is, for an arraywith Δx=0.2 feet at 3 ft/sec velocity the maximum array response willoccur at 3π/Δx=47.1 rad/sec where at 10 ft/sec velocity the maximumresponse will occur 10π/Δx=157 rad/sec. If the frequency isnon-dimensionalized in this manner, the maximum array response willalways occur at fΔx/u=0.5 regardless of the velocity. The advantage ofthis non-dimensionalization is that regardless of the velocity, thesection of the k-_(ω) plot that yields the maximum array response can beidentified and used.

Referring to step 62 of FIG. 3, knowing the calibration function and therelationship of each of the factors in the calibration function, themeasured velocity of the flow Uc(t) and measured volumetric flow (VF)signals may be calibrated knowing the actual or empirical relationshipof each of the relationships of the calibration function to provide amore accurate flow velocity Uc(t) and volumetric flow (VF).

FIG. 9

FIG. 9 illustrates empirical data representative of a family ofcalibration curves for a plurality of classes of flow meter of thepresent invention, described herein before, used to calibrate eachrespective class of meter. Each class of meter is represented or definedby the pipe that the flow meter is measuring. For example, one class isrepresented by a 4 inch ID, schedule 10 that is represented by thecalibration curve 100. Each calibration curve using empirical datacollected for a particular class of flow meters is defined by theequation C₀+C₁/Re^C₂ (Correction Function), wherein each class have aunique value for each of the coefficients C₀, C₁ and C₂. Re is theReynolds number of the flow propagating through the pipe. TheCalibration Curves are defined by Percent Error or Offset versus theReynolds number of the fluid, which is related to the velocity of thefluid flow as shown in FIG. 9. For example,V_(corrected)=V_(measured)/(Offset+1), the Offset=C₀+C₁/RE^C₂, andRe=0.00774×ρxV×ID/μ, where 0.007742=Combined conversion factor V (ft/sto m/s) and ID(in to m).

Each calibration curve includes all the factors or terms of thecalibration correction function described hereinbefore. All meterswithin the same class are calibrated using the same calibration curve,defined by the correction function.

As shown in FIG. 9, the measured velocity is corrected in accordancewith the corresponding calibration curve. For example, the measuredoutput velocity for a meter mounted to a 4 inch ID, 40 schedule pipehaving a flow with a Reynolds number of 5.0E+05 is corrected for a 4.50%offset.

Each sensor head includes 3 numbers representative of each of the threecoefficients C0, C1 and C2 of the “Correction Function”. Thesecalibration numbers are pre-programmed, or entered into the processor 24via line 38 a, for example, to calibrate the flow meter 10. This enablesany sensor head 16 of a different classes to be used with any processor24. Therefore the processor 24 are independent of the pipes beingmeasured.

The pressure sensors 18-21 of FIG. 1 described herein may be any type ofpressure sensor, capable of measuring the unsteady (or ac or dynamic)pressures within a pipe 14, such as piezoelectric, optical, capacitive,resistive (e.g., Wheatstone bridge), accelerometers (or geophones),velocity measuring devices, displacement measuring devices, etc. Ifoptical pressure sensors are used, the sensors 18-21 may be Bragggrating based pressure sensors, such as that described in U.S. patentapplication, Ser. No. 08/925,598, entitled “High Sensitivity Fiber OpticPressure Sensor For Use In Harsh Environments”, filed Sept. 8, 1997, nowU.S. Pat. No. 6,016,702, and in U.S. patent application, Ser. No.10/224,821, entitled “Non-Intrusive Fiber Optic Pressure Sensor forMeasuring Unsteady Pressures within a Pipe”, which are incorporatedherein by reference. In an embodiment of the present invention thatutilizes fiber optics as the pressure sensors 14 they may be connectedindividually or may be multiplexed along one or more optical fibersusing wavelength division multiplexing (WDM), time division multiplexing(TDM), or any other optical multiplexing techniques.

In certain embodiments of the present invention, a piezo-electronicpressure transducer may be used as one or more of the pressure sensors15-18 and it may measure the unsteady (or dynamic or ac) pressurevariations inside the pipe 14 by measuring the pressure levels inside ofthe pipe. These sensors may be ported within the pipe to make directcontact with the process flow 12. In an embodiment of the presentinvention, the sensors comprise pressure sensors manufactured by PCBPiezotronics. In one pressure sensor there are integrated circuitpiezoelectric voltage mode-type sensors that feature built-inmicroelectronic amplifiers, and convert the high-impedance charge into alow-impedance voltage output. Specifically, a Model 106B manufactured byPCB Piezotronics is used which is a high sensitivity, accelerationcompensated integrated circuit piezoelectric quartz pressure sensorsuitable for measuring low pressure acoustic phenomena in hydraulic andpneumatic systems.

It is also within the scope of the present invention that any strainsensing technique may be used to measure the variations in strain in thepipe, such as highly sensitive piezoelectric, electronic or electric,strain gages and piezo-resistive strain gages attached to the pipe 14.Other strain gages include resistive foil type gages having a race trackconfiguration similar to that disclosed U.S. patent application Ser. No.09/344,094, filed Jun. 25, 1999, now U.S. Pat. No. 6,354,147, which isincorporated herein by reference. The invention also contemplates straingages being disposed about a predetermined portion of the circumferenceof pipe 14. The axial placement of and separation distance ΔX₁, ΔX₂between the strain sensors are determined as described herein above.

It is also within the scope of the present invention that any otherstrain sensing technique may be used to measure the variations in strainin the pipe, such as highly sensitive piezoelectric, electronic orelectric, strain gages attached to or embedded in the pipe 14.

The scope of the invention is intended to include using other types orkinds of sensors including ultrasonic sensors similar to that disclosedin CC-0680 (Express Mail No. EV 286 928 152 US) and U.S. patentapplication Ser. No. 60/439,715, filed Jan. 13, 2003. The other types orkinds of sensors may sense or measure any parameter that converts withina flow. For example, any inhomogeneities, including temperature,particles, turbulence eddies, acoustic variations or disturbances.

Scope of the Invention

The dimensions and/or geometries for any of the embodiments describedherein are merely for illustrative purposes and, as such, any otherdimensions and/or geometries may be used if desired, depending on theapplication, size, performance, manufacturing requirements, or otherfactors, in view of the teachings herein.

It should be understood that, unless stated otherwise herein, any of thefeatures, characteristics, alternatives or modifications describedregarding a particular embodiment herein may also be applied, used, orincorporated with any other embodiment described herein. Also, thedrawings herein are not drawn to scale.

Although the invention has been described and illustrated with respectto exemplary embodiments thereof, the foregoing and various otheradditions and omissions may be made therein and thereto withoutdeparting from the spirit and scope of the present invention.

1. A method of determining an average flow rate of a fluid flowing inthe pipe, said method comprising: measuring unsteady pressures using anarray of sensors, wherein each sensor is spaced at different axiallocations along the pipe; determining, in response to the measuredunsteady pressures, a measured flow rate of the fluid flow; and relatingthe measured flow rate to the average flow rate of the fluid flow usinga calibration correction function based on non-dimensional parametersthat characterize the array of sensors, the pipe, and the fluid flowingin the pipe to determine the average flow rate, wherein the calibrationcorrection function depends on a Reynolds number that characterizes thefluid flow in the pipe, and a ratio fΔx/U_(meas) of usable frequenciesin relation to the sensor spacing (Δx) and the measured flow rate(U_(meas)); and wherein the measured flow rate of the fluid flow isdetermined using an array processing algorithm.
 2. The method accordingto claim 1, further includes determining the average volumetric flowrate (Q) of the fluid flow based on the equation:Q=A*U _(av), where A is a cross sectional area of the pipe's innerdiameter and U_(av) is the average flow rate.
 3. The method according toclaim 1, wherein the relating the measured flow rate to the average flowrate includes determining the average flow rate (U_(av)) based on theequation:U _(av)=the calibration correction function*U _(meas), where U_(meas) isa measured flow rate.
 4. The method according to claim 3, wherein themeasured flow rate of the fluid flow is determined by measuring a slopeof a convective ridge in a k-ω plane.
 5. The method according to claim1, wherein the sensors of the array of sensors include strain sensors orpressure sensors.
 6. The method according to claim 1, wherein the arrayof sensors include at least 3 sensors.
 7. The method according to claim1, wherein the array of sensors include at least 4, 5, 6, 7, 8 , 9, 10,11, 12, 13, 14, 15, or 16 sensors.
 8. The method according to claim 1,wherein the sensors are clamped onto the pipe.
 9. The method accordingto claim 1, wherein the unsteady pressures are vortical disturbanceswith the fluid flow.
 10. A flow meter for determining an average flowrate of a fluid flowing in the pipe, said flow meter comprising: anarray of sensors having an array of sensors for measuring unsteadypressures to determine a measured flow rate of the fluid, wherein eachsensor is spaced at different axial locations along the pipe; and aprocessor for relating the measured flow rate to the average flow rateof the fluid flow using a calibration correction function based onnon-dimensional parameters that characterize array of sensors, the pipe,and the fluid flowing in the pipe to determine the average flow rate,wherein the calibration correction function depends on a ratiofΔx/U_(meas) of usable frequencies in relation to the sensor spacing(Δx) and the measured flow rate (U_(meas)); and wherein the measuredflow rate of fluid flow is determined using an array processingalgorithm.
 11. The flow meter according to claim 10, wherein thecalibration correction function depends on a Reynolds number thatcharacterizes the fluid flow in the pipe, and a ratio fΔx/U_(meas) ofusable frequencies in relation to the sensor spacing (Δx) and themeasured flow rate (U_(meas)).
 12. The flow meter according to claim 10,wherein the average flow rate is an average volumetric flow rate (Q) andthe processor determines the average volumetric flow rate (Q) based onthe equation:Q=A*U _(av), where A is a cross sectional area of the pipe's innerdiameter and U_(av) is an average flow rate.
 13. The flow meteraccording to claim 10, wherein the calibration correction functionmodule determines the average flow velocity (U_(av)) based on theequation:U _(av)=the calibration correction function*U _(meas), where U_(meas) isa measured flow rate.
 14. The flow meter according to claim 13, whereinthe measured flow rate of fluid flow is determined by measuring a slopeof a convective ridge in a k-ω plane.
 15. The flow meter according toclaim 10, wherein the sensors of the array of sensors include strainsensors or pressure sensors.
 16. The flow meter according to claim 10,wherein the array of sensors include at least 3 sensors.
 17. The flowmeter according to claim 10, wherein the array of sensors include atleast 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, or 16 sensors.
 18. Theflow meter according to claim 10, wherein the sensors are clamped ontothe pipe.
 19. The flow meter according to claim 10, wherein the unsteadypressures are vortical disturbances with the fluid flow.